Polar codes have been proposed to be used as channel codes for wireless communications, including for uplink and downlink enhanced mobile broadband (eMBB) control channel coding for 5G air interface. Polar codes have been found to have performance that is at least comparable with state-of-the-art error correction codes, and have relatively low encoding complexity. An example is described by E. Arikan in “Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels,” IEEE Trans. Inf. Theory, vol. 55, no. 7, pp. 3051-3073, 2009.
Parity-check (PC) polar codes employ assistant bits to improve the performance of polar codes. There are different variations of polar codes that can be considered as special cases of PC-polar codes. For example, cyclic redundancy check (CRC) polar codes are a type of PC-polar code in which the assistant bits are calculated using a CRC polynomial. With PC-polar codes, the bits are transmitted in sub-channels, which may be referred to as follows: the information sub-channels are used to carry the information bits; the frozen sub-channels carry deterministic bits (referred to as frozen bits); and the assistant sub-channels carry assistant bits. For PC-polar codes, the assistant bits may be related to the information bits using PC equations. Different performance aspects (e.g., power consumption) of PC-polar codes depend on the selection of PC sub-channels and the PC equations.
With PC-polar codes (e.g., PC-frozen polar codes, CRC-polar codes or other types using assistant bits), the information bits and the assistant bits are placed in the information sub-channels and all are treated as information bits when the decoder performs successive cancellation list (SCL) decoding. At the end of decoding, each list path is checked to see if the parity check is passed. A path which does not pass the check will be considered as wrong or unsuccessful. If no path passes checking, a decoding failure is declared. If none of the paths passes the check, this means that there is at least one assistant bit that violates the PC equations for all paths. If the decoder had checked the PC equation for this one assistant bit earlier in decoding, the decoder could have avoided all the unnecessary subsequent decoding calculations and terminated the decoding early by declaring a decoding failure after encountering this one assistant bit. This is referred to as early termination (ET) and can significantly mitigate the decoding complexity. Distribution of assistant bits directly affects the ET performance, including whether ET is even possible.